There was actually a huge fight between J. Edgar Hoover and Clyde Tolson in a hotel during one of their trips. According to Clint Eastwood, there are several testimonies of maids that talked about the room being destroyed after the discussion. However, writer Dustin Lance Black dramatized the content of the argument.
Armie Hammer, who plays Clyde Tolson, is the great-grandson of Occidental Petroleum tycoon Armand Hammer. In his biography of Hammer (the tycoon, not the actor) called "Dossier: The Secret History of Armand Hammer," author Edward Jay Epstein reported that the tycoon had a multi-decade history of being scrutinized and suspected of Soviet ties by J. Edgar Hoover. Armie stated in an interview that he took the role to avenge that scrutiny.
The closing lines of the film, "Most clearly I remember your eyes, with a kind of teasing smile in them, and the feeling of that soft spot just north-east of the corner of your mouth against my lips..." is a quote from a letter from Lorena Hickok to Eleanor Roosevelt.
Clint Eastwood is famous for shooting the screenplays he directs almost verbatim, not making changes. Dustin Lance Black has admitted he didn't like that, arguing he loves to discuss the screenplay with the director and improving it together with suggestions.
When J. Edgar Hoover and his mother leave the Strand Theatre following the premiere of 'G' Men, a theatre marquee across Times Square announces the Eltinge Follies. Julian Eltinge was a famous female impersonator and drag performer in the early 20th century and had his own theater on 42nd Street. The Eltinge Theatre depicted in this film opened in 1912 and was renamed the Empire Theatre in 1942. It is now part of the AMC Empire 25 complex.
Stephen Root plays Arthur Koehler, the forensics expert who in the movie manages to identify where the piece of wood that might help identify the kidnapper in Lindberg's case was bought. In TV biopic of Lyndon B. Johnson, All the Way (2016) , Root plays J. Edgar Hoover himself.
Actor DiCaprio and director Eastwood had a falling out during shooting. When the actor requested a retake, director Eastwood called it a wrap and walked away. Both stars were cool to each other for the rest of the film.